Group-valued measures on coarse-grained quantum logics |
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Authors: | Anna De Simone Pavel Pták |
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Institution: | (1) Dipartimento di Matematica, e Statistica, Università degli Studi, “Federico II” di Napoli, 80126 Napoli, Italy;(2) Faculty of Electrical Eng., Department of Mathematics, Czech Technical University, 166 27 Prague 6, Czech Republic |
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Abstract: | In 3] it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure,
over the entire power algebra. Later (9]) this result was re-proved (and further improved on) and, moreover, the non-negative
measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique
of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained
quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely
different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms
of cyclic coarse-grained quantum logics. |
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Keywords: | coarse-grained quantum logic group-valued measure measure extension |
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